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↓⊳∖∣∽↙⋎∶ ≤≥↿∖⇉⋎∃⊳↓∖⊽∪↿⊲↓⊔⋏∙≟↿↓⋯↿↿↓⊔⋅⊔↓⋜↧⋏∙≟⋯⋅↿⊲⊔∼∐∢⊾↓∠⇂⊲↓⊔↿↓↥⋖⋅∖∖⋎↕↓↕∠⇂⇂⋅↓⋅⋜↧↓↥↓∢⊾↕≻ ∐∣∶∐⋎⊳∪⊔∢⊾≼⇍⋜⋯↓⋅∢⋅∠⊔∐∼⋖⊾↿↓↕⋖⋅≼∙⋖⋟↓↥∠⇂↕↿↕⋖⋟↓↥∩∩↿∪ This radius should be compared with the radius of the standing shock where the wind terminates. | Noting that the magnetic field in the wind frame is $B'=B/\gamma$, one can reduce the condition (6) to This radius should be compared with the radius of the standing shock where the wind terminates. |
One can place the upper limit on this radius bv equating the magnetic pressure in the wind to the rani pressure of the medium. Επ=(M7. where p=Apo efem? is the density of the interstcllar gas. 1=10015 kms the velocity of pulsar through it. | One can place the upper limit on this radius by equating the magnetic pressure in the wind to the ram pressure of the medium, $B^2/8\pi=\rho V^2$, where $\rho=1\rho_0$ $^3$ is the density of the interstellar gas, $V=100V_2$ km/s the velocity of pulsar through it. |
Substituting Lq.(8). one obtains The radius of the terminating shock may be less than (10) if the pulsar is surrounded. by a dense plerion. | Substituting Eq.(8), one obtains The radius of the terminating shock may be less than (10) if the pulsar is surrounded by a dense plerion. |
Comparing LEq.(10) with I5q.(0) one can see that [MS waves in the pulsar wind mav be considered. in. MIID approximation. | Comparing Eq.(10) with Eq.(9) one can see that FMS waves in the pulsar wind may be considered in MHD approximation. |
The wave may decay in multiple shocks that arise as a result of nonlinear steepening. | The wave may decay in multiple shocks that arise as a result of nonlinear steepening. |
"Transforming the characteristic nonlinear scale (7) to the pulsar frame. one gels The magnetizationIn] parameter of the wind depends on the plasma density. | Transforming the characteristic nonlinear scale (7) to the pulsar frame, one gets The magnetization parameter of the wind depends on the plasma density. |
In the pulsar frame. one can conveniently express the density. ΑΔ=one. via the cdimensionless multiplicity factor. &. as 3efore the multiple shocks arise. the pulsar wind is cold. wsomn. and propagates with a constant Lorentz factor +o. | In the pulsar frame, one can conveniently express the density, $N=n\gamma$, via the dimensionless multiplicity factor, $\kappa$, as Before the multiple shocks arise, the pulsar wind is cold, $w=mn$, and propagates with a constant Lorentz factor $\gamma_0$ . |
The magnetization parameter remains constant. where ως=ο£m is the evrofrequeney at the light cvlinder. | The magnetization parameter remains constant, where $\omega_L\equiv eB_L/m$ is the gyrofrequency at the light cylinder. |
Now one can write the shock formation distance as | Now one can write the shock formation distance as |
han that induced by carbon-oxvecn phase separation. | than that induced by carbon-oxygen phase separation. |
Tn particular. bx log(L/L.)zcLO. the luninosity at which the faint peal: of the white dwiuf huuinositv Muction im NGC 6791 is located. the release of energy rom) 7?Ne sedimeutation markedly slows down the cooling rate of the more massive white dwarfs. which. vecause of their short pre-wlite dwiuf times. populate he faint eud of the white dwarf Iuninositv function of he cluster. | In particular, by $\log(L/L_{\sun}) \approx -4.0$, the luminosity at which the faint peak of the white dwarf luminosity function in NGC 6791 is located, the release of energy from $^{22}$ Ne sedimentation markedly slows down the cooling rate of the more massive white dwarfs, which, because of their short pre-white dwarf times, populate the faint end of the white dwarf luminosity function of the cluster. |
For our more massive sequences aud at the netallicity of the cluster (Z~ 0.01). we fud that the delavs frou ??Ne sedimentation alone range from 1.10 o 1.50 Car and z Lad Cyr at loe(L/L.)~--1.0 22d 1.2. respectively. | For our more massive sequences and at the metallicity of the cluster $Z\simeq 0.04$ ), we find that the delays from $^{22}$ Ne sedimentation alone range from 1.10 to 1.50 Gyr and $\approx$ 1.80 Gyr at $\log(L/L_{\sun}) \approx -4.0$ and $-4.2$, respectively. |
These delays together with the delays resulting from carbou-oxvecn phase separation. are of the order of what is required to solve the age discrepaucy in NGC 6791 iaBero et al. | These delays together with the delays resulting from carbon-oxygen phase separation, are of the order of what is required to solve the age discrepancy in NGC 6791 a–Berro et al. |
2010). | 2010). |
The «clay iu thecooling rate of white dwarfs resulting frou 77Ne sediiueutation 15 iuportant aud poiuts out the necessity of incorporating this energy source in the calculation of detailed white dwart cooling sequences. particularly in the case of white dwarts populating metal-rich clusters. | The delay in thecooling rate of white dwarfs resulting from $^{22}$ Ne sedimentation is important and points out the necessity of incorporating this energy source in the calculation of detailed white dwarf cooling sequences, particularly in the case of white dwarfs populating metal-rich clusters. |
Because of the relevance of the 7?Ne sedimentation for the cooling of white dwarfs. we find instructive to estimate the lowest metallicity for which ??Ne sedimentation starts to affect significantly the cooling times of white dwarts. | Because of the relevance of the $^{22}$ Ne sedimentation for the cooling of white dwarfs, we find instructive to estimate the lowest metallicity for which $^{22}$ Ne sedimentation starts to affect significantly the cooling times of white dwarfs. |
To this cud. we compute additional cooling sequences for initial Ne abuudauces of 0.01 and 0.005. | To this end, we compute additional cooling sequences for initial $^{22}$ Ne abundances of 0.01 and 0.005. |
For the case of an initial ??Ne abundance of 0.01. 7?Ne sedimentation increases the cooling time of our 0.5219AL. sequence that considers latent heat and carbon-oxvecn phase separation by at most 2%. | For the case of an initial $^{22}$ Ne abundance of 0.01, $^{22}$ Ne sedimentation increases the cooling time of our $0.5249 \, M_{\sun}$ sequence that considers latent heat and carbon-oxygen phase separation by at most $\%$ . |
The magnitude of the delavs are larger for more nassive white dwarfs. reaching A and S( for the 1051 aud 1.0A. sequences. respectively. | The magnitude of the delays are larger for more massive white dwarfs, reaching $\%$ and $\%$ for the 0.7051 and $1.0 \, M_{\sun}$ sequences, respectively. |
For these two stellar masses. the resulting delays are 3% and IX for à 7?Ne abundances of 0.005. | For these two stellar masses, the resulting delays are $\%$ and $\%$ for a $^{22}$ Ne abundances of 0.005. |
We conclude that. or initial Ne abundances smaller than z0.01. Νο sedimentation has a minor iirpact on white dwarf cooling nues. except for rather massive white dwarts for which j0n-neelieible delavs (but smaller than 8%) are found even for 77Ne abundances of 0.005. | We conclude that, for initial $^{22}$ Ne abundances smaller than $\approx
0.01$, $^{22}$ Ne sedimentation has a minor impact on white dwarf cooling times, except for rather massive white dwarfs for which non-negligible delays (but smaller than $8\%$ ) are found even for $^{22}$ Ne abundances of 0.005. |
Finally. to account for possible uncertainties iu the actual value of the diffusion coefficient of 77Ne (Delove Bildsten 2002). we compute additional cooling sequences for which we iultiplv aud divide the diffusion coefücieut by a factor of 2. | Finally, to account for possible uncertainties in the actual value of the diffusion coefficient of $^{22}$ Ne (Deloye Bildsten 2002), we compute additional cooling sequences for which we multiply and divide the diffusion coefficient by a factor of 2. |
The resulting iupacts on the cooling time for the case in which Z0.03 can be seen iu Fie. | The resulting impacts on the cooling time for the case in which $Z=0.03$ can be seen in Fig. |
3 for the 0.7051 aud the 0.5219ΑΕ. sequences that consider latent heat. carbon-oxvecn phase separation aud ??Noe sedimentation. | \ref{edad_003} for the 0.7051 and the $0.5249 \, M_{\sun}$ sequences that consider latent heat, carbon-oxygen phase separation and $^{22}$ Ne sedimentation. |
Ti6 grav region shows the extent o which the cooling curves vary when the diffusion coefficient is change within this rauge of values. | The gray region shows the extent to which the cooling curves vary when the diffusion coefficient is changed within this range of values. |
For he iore massive seqence and at log(L/L.)=1.5 ido. the cooling tiues change by less than S and 5%.έν aud by 1T and δν respectively. | For the more massive sequence and at $\log(L/L_{\sun}) = -4.5$ and $-4$, the cooling times change by less than $8\%$ and $-5\%$, and by $17\%$ and $-8\%$ , respectively. |
For the less hassive sequence. the changes remain below 7%. | For the less massive sequence, the changes remain below $7\%$. |
In the case of the 1.0AL... sequence. an merease m D, by a factor of 2 causes a maxim age difference of zz20% in the πληναν rauee from loe(L/L.)=3 to 3.5. | In the case of the $1.0 \, M_{\sun}$ sequence, an increase in $D_{\rm s}$ by a factor of 2 causes a maximum age difference of $\approx 20 \%$ in the luminosity range from $\log(L/L_{\sun}) \approx -3$ to $-3.5$. |
It is clear that uncertainties in the diffusion cocfiicicut larger iu a factor of 2 will affect the cooling time considerably. ouwtieularly for our most massive white dwarf sequences. | It is clear that uncertainties in the diffusion coefficient larger than a factor of 2 will affect the cooling time considerably, particularly for our most massive white dwarf sequences. |
The use of white dwarts as reliable cosmic clocks to date Galactic stellar populations has been recently thrown iuto doubt by a new observational determination of the white dwarf huninositv function in the old. metalrich open cluster NGC 6791 (Bedin et al. | The use of white dwarfs as reliable cosmic clocks to date Galactic stellar populations has been recently thrown into doubt by a new observational determination of the white dwarf luminosity function in the old, metal-rich open cluster NGC 6791 (Bedin et al. |
2008). the age of which as derived from the main sequence turn- technique (8 Cir) markedly disagrees with the age derived from the termination of the white dwarf cooling sequence (6 Carr). | 2008), the age of which as derived from the main sequence turn-off technique (8 Gyr) markedly disagrees with the age derived from the termination of the white dwarf cooling sequence (6 Gyr). |
This discrepancy poiuts out at a mussing plysical process in the standard treatiuneut of white dwarf evolution. | This discrepancy points out at a missing physical process in the standard treatment of white dwarf evolution. |
In view of the lieh metallicity characterizing NCC 6791 (Zz 0.01). the eravitational settling of ??Ne coustitutes the most viable process that cau decrease the cooling rate of cool white dwarts. | In view of the high metallicity characterizing NGC 6791 $Z\approx 0.04$ ), the gravitational settling of $^{22}$ Ne constitutes the most viable process that can decrease the cooling rate of cool white dwarfs. |
ludeed. as first shown bv Iseru et al. ( | Indeed, as first shown by Isern et al. ( |
L991) aud later bv Delove Bildsten (2002) aud. CarciaaBerro et al. ( | 1991) and later by Deloye Bildsten (2002) and a–Berro et al. ( |
2008). the slow gravitational settling of Νο iu the liquid phase releases enough euergv as to appreciably VAow down the cooling rate of white dwarfs in inetalaichi ‘asters like NGC 6791. | 2008), the slow gravitational settling of $^{22}$ Ne in the liquid phase releases enough energy as to appreciably slow down the cooling rate of white dwarfs in metal-rich clusters like NGC 6791. |
Motivated by these considerations. we lave presened a exkl of white dwarf evolutionary sequences tlat incorporates for the first time the enerev contributioIs arising frou both 77Ne sedimentation aud carbou-oxvgen phase separation. | Motivated by these considerations, we have presented a grid of white dwarf evolutionary sequences that incorporates for the first time the energy contributions arising from both $^{22}$ Ne sedimentation and carbon-oxygen phase separation. |
The erid covers the cutire mass rauge expected for carbon-oxvecn white dwarts. from 0.52 1.0 M... and itis based on a detailed aud self-cousistetreatinent of these cuerey sources. | The grid covers the entire mass range expected for carbon-oxygen white dwarfs, from 0.52 to $1.0 \,
M_{\sun}$ , and it is based on a detailed and self-consistenttreatment of these energy sources. |
Except for the 1.0A. sequence. the listory of progenitor stars has been taken into account bv evolving iuitial stellarconfieuratio in the mass range d to SAL. from the ZAMS all t | Except for the $1.0 \, M_{\sun}$ sequence, the history of progenitor stars has been taken into account by evolving initial stellarconfigurations in the mass range 1 to $5 \,
M_{\sun}$ from the ZAMS all the |
Iu this subsection let us cousider the parasitic interfereuce ellect while observing a poiut-like source. | In this subsection let us consider the parasitic interference effect while observing a point-like source. |
The unresolved object is described by its angular position in the sky noted @point. with respect to the line of sight. and its monochromatic fluxnoted Ipji(A). | The unresolved object is described by its angular position in the sky noted $\boldsymbol{\alpha_{\rm point}}$, with respect to the line of sight, and its monochromatic fluxnoted $_{\rm point}(\lambda)$. |
The chromatic brightness distribution cau be represented iu the same way as in the resolved source case. such that ouly one tilted) wavelront originates [roin the source : | The chromatic brightness distribution can be represented in the same way as in the resolved source case, such that only one tilted wavefront originates from the source : |
outburst. aud of its magnitude. | outburst, and of its magnitude. |
Also. oue of the possible routes to the formation of chondrules within our model gives results which are consistent. with the typical size of chioudrules. | Also, one of the possible routes to the formation of chondrules within our model gives results which are consistent with the typical size of chondrules. |
There is considerable scope for further work to determine the extent to which our arguimeuts are supported by more detailed aud euautitative iuvestigations. | There is considerable scope for further work to determine the extent to which our arguments are supported by more detailed and quantitative investigations. |
Also because of the complexity of the processes involved iu trausformiug our hiypotliesised juvenile planets into a mature planetary system. there may be other mechauisius which we have uot euvisaged. | Also because of the complexity of the processes involved in transforming our hypothesised juvenile planets into a mature planetary system, there may be other mechanisms which we have not envisaged. |
Our moclel raises new questions which are likely to be a fertile erouud for subsequent research. | Our model raises new questions which are likely to be a fertile ground for subsequent research. |
Support from Veteuskapsraddet is gratefully ackuowledgect. | Support from det is gratefully acknowledged. |
compactly supported curreut sources. these loops are occasionally unstable. and fare as open pronmiünences. as shown iu the left column of Fig. | compactly supported current sources, these loops are occasionally unstable, and flare as open prominences, as shown in the left column of Fig. |
1. | 4. |
This suggests that open flux-tubes nieht form frou loops iu the torus maguctosplere connecting the black hole aud the torus. sketched iu the right column of Fig. | This suggests that open flux-tubes might form from loops in the torus magnetosphere connecting the black hole and the torus, sketched in the right column of Fig. |
l. | 4. |
Tf so. this eives rise to an inner open fiux-tube supported by the magnetic moment ofthe black hole aud outer open fiux-tuboe supported by the magnetic moment of the ner face of the torus. | If so, this gives rise to an inner open flux-tube supported by the magnetic moment of the black hole and outer open flux-tube supported by the magnetic moment of the inner face of the torus. |
Creating open fiux-tubes in the fashion Is accompanied by an algebraic constraint: the ner aud outer fiux-tubes carry a daguetic flux which is equal in magnitude and opposite in sign. | Creating open flux-tubes in the fashion is accompanied by an algebraic constraint: the inner and outer flux-tubes carry a magnetic flux which is equal in magnitude and opposite in sign. |
Applying ⋅ ⋅⋅ ∣≻ ↑∐↸∖↴∖↴⋜⋯∐∖⋜↧↴∖↴⋅↖⇁∐∏≻↑∪↑↕↸⊳↴⋝∪∏∐≼⋜∐⋅∙↖⇁↸⊳∪∐≺∐⊓∪∐⊽∣−∶∩↑∪∐↸∖≺∏↕↑∏∪↖↖⇁↕↥⋅∪⋯↑∐↸∖↑∪↥⋅∏↴∖↴ and this is expected to be an approximation to within order unity πο obtain global current closure in the form of 7=J|Ip Opa... where Or denotes the augular velocity of the torus. | Applying the same asymptotic boundary condition $j^2=0$ to the outflow from the torus – and this is expected to be an approximation to within order unity – we obtain global current closure in the form of $I_-=I_+=I_T=\Omega_TA_\phi$ , where $\Omega_T$ denotes the angular velocity of the torus. |
The result is a differentially rotating eap between foremenutioned two equilibriun sections. oue attached to infiütv and the other attached to the horizon. with a Faraday-nduced poteutial drop AV=(0,οJA, | The result is a differentially rotating gap between forementioned two equilibrium sections, one attached to infinity and the other attached to the horizon, with a Faraday-induced potential drop $\Delta V=(\Omega_+-\Omega_-)A_\phi$. |
The power dissipated in this [m]gap becomes Thus. a gap forms with macroscopic dissipation whenever the black hole spius more rapidly thaw the angular velocity of tho torus? Of some interest is the formation of the eap (ο7 207) while being in a state of lyper-accretion (25,< O5). | The power dissipated in this gap becomes Thus, a gap forms with macroscopic dissipation whenever the black hole spins more rapidly than the angular velocity of the \cite{mvp01b}
Of some interest is the formation of the gap $(\Omega_H>2\Omega_T$ ) while being in a state of hyper-accretion $(\Omega_H<\Omega_H^*$ ). |
Attributing the power released in the eap to the input to the observed GRB aud afterglow cussions. sugecsts the possibility for afterglow cinissious to short bursts. | Attributing the power released in the gap to the input to the observed GRB and afterglow emissions, suggests the possibility for afterglow emissions to short bursts. |
Unless the cuviroument to short bursts is dramatically different from long bursts. IIETE-II should see afterelows to short bursts as well? Recent analysis of achromatic breaks in a sub-smuuple of CRB liehteurves indicates that these cunissious are beamed. aud that their true fluence Ly, is standard Gwith a dynamic range of about one decade) at few times {0 ores 219 | Unless the environment to short bursts is dramatically different from long bursts, HETE-II should see afterglows to short bursts as \cite{mvp01a}
Recent analysis of achromatic breaks in a sub-sample of GRB lightcurves indicates that these emissions are beamed, and that their true fluence $E_{grb}$ is standard (with a dynamic range of about one decade) at few times $10^{50}$ ergs \cite{fra01,pan01}. |
At the sune time. the opening anele displays a rather wide dynamic range. )etween a few degrees and a few tens of degrees. | At the same time, the opening angle displays a rather wide dynamic range, between a few degrees and a few tens of degrees. |
Iu". we cousider a geometrically staudard inner region iu the vicinity of the black hole. when the torus is thick relative to the size of the black tole. | In \cite{mvp01c}, we consider a geometrically standard inner region in the vicinity of the black hole, when the torus is thick relative to the size of the black hole. |
Iu this event. the opening anele of the open flus-tube on the horizon cohunensurate with the true cussions m GRBs is about 35". | In this event, the opening angle of the open flux-tube on the horizon commensurate with the true emissions in GRBs is about $35^o$. |
Collimatiou of his fiux-tube down to au opening angle 0; ou the celestial sphere may derive roni Winds comine off the torus. possibly so alone foroiieutioned outer This will account for a true output iu outflow of about Lyn(n/0i)e1 | Collimation of this flux-tube down to an opening angle $\theta_j$ on the celestial sphere may derive from winds coming off the torus, possibly so along forementioned outer flux-tube.This will account for a true output in outflow of about $E_{grb}(\theta_H/\theta_j)\epsilon^{-1}$ , |
component of the field equals the poliodal component at the inner edge of the disc (2)OTA. lor BP Tau and 2;~1.58. For V2129 Oph). | component of the field equals the poliodal component at the inner edge of the disc $R_t \sim 0.7R_{co}$ for BP Tau and $R_t \sim 0.5R_{co}$ for V2129 Oph). |
However. for a better comparison with the extrapolatect fields we consider mocified ancl tilted dipole fields. i.e. dipole fields with a source surface. tilted by he same amount as the dipole component in both stars. | However, for a better comparison with the extrapolated fields we consider modified and tilted dipole fields, i.e. dipole fields with a source surface, tilted by the same amount as the dipole component in both stars. |
Once the dipole field. been tilted. the magnetic field. is no longer axisvmumetric in the stars equatorial plane. and herefore D. is no longer uniform in azimuth at a fixed radius. | Once the dipole field been tilted, the magnetic field is no longer axisymmetric in the stars equatorial plane, and therefore $B_z$ is no longer uniform in azimuth at a fixed radius. |
At each radius r we therefore take the average of the square of D. for use in equation (19))? (note that we follow he same procedure for the extrapolated fields: discussed xdow). | At each radius $r$ we therefore take the average of the square of $B_z$ for use in equation \ref{trunc}) (note that we follow the same procedure for the extrapolated fields discussed below). |
The dash-dot lines in Fig. | The dash-dot lines in Fig. |
6 represent such tilted dipoles. with the disc truncation radius being slightly closer othe stellar surface for such fields due to the non-uniformity of D. in azimuth. | \ref{rt} represent such tilted dipoles, with the disc truncation radius being slightly closer to the stellar surface for such fields due to the non-uniformity of $B_z$ in azimuth. |
In Fig. | In Fig. |
6 (and Figs. | \ref{rt} (and Figs. |
δ and 7. below) we rave chosen to set. As=20/1. in order to minimise the ellects of the source surface boundary condition upon the ield structure close to the accreting field regions. | \ref{bratio_small} and \ref{bratio_big} below) we have chosen to set $R_S = 20\,R_{\ast}$ in order to minimise the effects of the source surface boundary condition upon the field structure close to the accreting field regions. |
We have already seen in 833.1] that the [arger scale ield of BP Tau is similar to a dipole. but that the field of V2129 Oph shows significant departures [from such a simple field configuration. | We have already seen in 3.1 that the larger scale field of BP Tau is similar to a dipole, but that the field of V2129 Oph shows significant departures from such a simple field configuration. |
We therefore expect that the disc runcation radius calculated: using the extrapolated field of BP Tau will be similar to that of a dipole while £) or V2129 Oph may be dilferent. | We therefore expect that the disc truncation radius calculated using the extrapolated field of BP Tau will be similar to that of a dipole while $R_t$ for V2129 Oph may be different. |
The dotted lines in Fig. | The dotted lines in Fig. |
6 demonstrate that this is indeed the case. with 2) for DP Tau closely matched to that of the niocifiec dipole. | \ref{rt} demonstrate that this is indeed the case, with $R_t$ for BP Tau closely matched to that of the modified dipole. |
This is due to the strong dipole component of BP ‘Tau’s field. which contains of the magnetic enerey (?).. and is 4-imes stronger than the dipole component of V2129 Oph. | This is due to the strong dipole component of BP Tau's field, which contains of the magnetic energy \citep{don08a}, and is 4-times stronger than the dipole component of V2129 Oph. |
The calculated inner disc radius lor V2120 Oph is closer o the stellar surface than would be expected. for a dipole ield. | The calculated inner disc radius for V2129 Oph is closer to the stellar surface than would be expected for a dipole field. |
This is à reflection of the intrinsic field complexity of V2129 Oph. and the rapid. drop olf in field strength with wight above the stellar surface for its magnetic field. (see 855.2 below). | This is a reflection of the intrinsic field complexity of V2129 Oph, and the rapid drop off in field strength with height above the stellar surface for its magnetic field (see 5.2 below). |
When the magnetic field of the central star is xwticularly complex. as in the case of V2129 Oph. we find hat the inner disc is truncated closer to the stellar surface han would be expected from dipole magnetic field mocels. | When the magnetic field of the central star is particularly complex, as in the case of V2129 Oph, we find that the inner disc is truncated closer to the stellar surface than would be expected from dipole magnetic field models. |
Llowever. the use of equations such as (19)) in calculating disc truneation radii for individual stars should be treated with caution. | However, the use of equations such as \ref{trunc}) ) in calculating disc truncation radii for individual stars should be treated with caution. |
Firstly. the values of Z2; determined here are very sensitive to the assumed mass aecretion rates AL. which are poorly constrained. observationallv. | Firstly, the values of $R_t$ determined here are very sensitive to the assumed mass accretion rates $\dot{M}$, which are poorly constrained observationally. |
For example. only a [actor of 2 dillerence in our assumed. accretion rate for DP αι of 2.88107M.sr+ would change the inner disc radius [rom 4.8/2, to 3.943, or 5.92, depending on whether he accretion rate is increased or decreased: respectively. | For example, only a factor of 2 difference in our assumed accretion rate for BP Tau of $2.88 \times 10^{-8}\,{\rm M}_{\odot}{\rm yr}^{-1}$ would change the inner disc radius from $4.8R_{\ast}$ to $3.9R_{\ast}$ or $5.9R_{\ast}$ depending on whether the accretion rate is increased or decreased respectively. |
Secondly. equation (19)) assumes that the field. threading he dise is dominated by the vertical component. D.. and although this is the case for the dipole-ike large scale field of BP Tau. it is not true for V2129. Oph where the field ms a significant radial component at the stellar equatorial Xdane. | Secondly, equation \ref{trunc}) ) assumes that the field threading the disc is dominated by the vertical component $B_z$, and although this is the case for the dipole-like large scale field of BP Tau, it is not true for V2129 Oph where the field has a significant radial component at the stellar equatorial plane. |
Thus the shear within the cise of V2129 Oph may generate a significant toroidal component. invalidating the use of equation (19)). ancl suggesting that our qualitative calculation of the disc truncation radius is too simplistic. | Thus the shear within the disc of V2129 Oph may generate a significant toroidal component, invalidating the use of equation \ref{trunc}) ), and suggesting that our qualitative calculation of the disc truncation radius is too simplistic. |
An AULD simulation using the extrapolatecd fields as starting points would. be welcome here. in order to calculate inner disc radii more quantitatively. | An MHD simulation using the extrapolated fields as starting points would be welcome here, in order to calculate inner disc radii more quantitatively. |
However. our conclusion that the inner dise should be truncated at. or within. the location | However, our conclusion that the inner disc should be truncated at, or within, the location |
107 L. ealaxiecs will be measured. from z~ 0.5 to 2.5. | $^{13}$ $_{\odot}$ galaxies will be measured from $\sim$ 0.5 to 2.5. |
Galaxies with L3 1044 L. will be only accessible at z~0.1. | Galaxies with $\sim$ 3 $^{11}$ $_{\odot}$ will be only accessible at $\sim$ 0.1. |
The nature and number of the highest luminosity objects are important to test cosmological theories. and thus populating the high redshift bins with enough objects to ensure «124 Poisson noise (corresponding to 50 sources) is a critical driver for the size of the sample. and accordingly. the area required for the survey. | The nature and number of the highest luminosity objects are important to test cosmological theories, and thus populating the high redshift bins with enough objects to ensure $<$ $\%$ Poisson noise (corresponding to 50 sources) is a critical driver for the size of the sample, and accordingly, the area required for the survey. |
Based on our model. we see from. Lig. | Based on our model, we see from Fig. |
19. that to meet this ~14% goal for galaxies in the range LO - 107 Lat z«2.5. an area of 100 square degrees is the minimum required. | \ref{dn-350} that to meet this $\sim$ $\%$ goal for galaxies in the range $^{12}$ - $^{13}$ $_{\odot}$ at $<$ 2.5, an area of 100 square degrees is the minimum required. |
@ The vorv-deep The confusion-limited surveys will detect only ~7% of the CIB (1% for the vey-laree area survey). | $\bullet$ The very-deep The confusion-limited surveys will detect only $\sim$ $\%$ of the CIB $\%$ for the vey-large area survey). |
In this case. studying the Uuetuations will bring informations on the underlying source population. | In this case, studying the fluctuations will bring informations on the underlying source population. |
The redshift distribution of sources making the bulk of the CIDB and the Huctuations at 350 pim are very. similar. | The redshift distribution of sources making the bulk of the CIB and the fluctuations at 350 $\mu$ m are very similar. |
“Phus. the fluctuations will be the unique opportunity to get information. particularly on sources that dominate the CIB (sources with L~3 104 L.). i redshifts where they cannot be detected individually. | Thus, the fluctuations will be the unique opportunity to get information, particularly on sources that dominate the CIB (sources with $\sim$ 3 $^{11}$ $_{\odot}$ ), at redshifts where they cannot be detected individually. |
To detect and study them. a field with high signal-to-noise ratio is needed. | To detect and study them, a field with high signal-to-noise ratio is needed. |
Moreover. the size of the field should be large enough to try to detect the source clustering anc not only be limited to the Poissonian noise detection (which is about 4300 Jy? sr). | Moreover, the size of the field should be large enough to try to detect the source clustering and not only be limited to the Poissonian noise detection (which is about 4300 $^2$ /sr). |
Since the source clustering is expected at the scales between 1 and 5 degrees (Ixnox et al. | Since the source clustering is expected at the scales between 1 and 5 degrees (Knox et al. |
2001). a field of about S square degrees is the minimum required. | 2001), a field of about 8 square degrees is the minimum required. |
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